## 116 Reputation

12 years, 362 days

## verifying solutions of tan(x)=x...

Maple

so i need to check that these solutions are in fact solutions. they are obviously very close but i can't get the boolean output to be "true".

eqn1:=tan(x)=x;
N:=10;
soln_array:=Array(1..N):
for m from 1 to N do
this_soln:=fsolve( eqn1 , x=(m-1/2)*Pi..(m+1/2)*Pi );
soln_array[m]:=[this_soln, tan(this_soln)];
end do:
soln_array;
for m from 1 to N do
this_soln:=fsolve( eqn1 , x=(m-1/2)*Pi..(m+1/2)*Pi );
evalb(simplify(tan(this_soln)-this_soln)=0);
end do;

## Decimal to Fraction Converter...

Maple

In principle I think this should be pretty easy. I need to make a MAPLE code that uses loops and arrays to carry out the prcedure described here: http://people.revoledu.com/kardi/tutorial/ContinuedFraction/Decimal-Fraction-Conversion.htm

## Generating matrices...

Maple

I have to generate a set of antihermitian matrices and the entries the non-zero entries have to be randomly generated. i can generate one antihermitian matrix. but now i want to generate many of them and store them in an array.

my code is:

## Integral...

ok just trying to integrat something here

-[(tan(theta)) dtheta]/[sec(theta) (2cos(theta)-1)^(0.5) (1-cos(theta))] = (sqrt(Mgh/A)) t

and get to sec(theta) = 1 + sech (sqrt(Mgh/A)) t

## Get Maple To Check Diff Eqn...

Maple

ok so i have the differnetial equation

$\lambda^{2} (\frac{dx}{dt})^{2} = (cos{ \alpha} - x)(cos{ \beta} - x)$

where $x = cos{ \theta}$

and the solution is

$x = cos{ \alpha} sin^{2}{\frac{t}{2 \lambda}} + cos{ \beta} cos^{2}{\frac{t}{2 \lambda}}$

please show you're working cos that's where im getting lost

now i want to use maple to show this is the solution to the eqn.

how do i do this???

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